, We denote by A the set N \ A, and for any positive integer k we set kA = {k × a | a ? A}. An A-ear-decomposition of a graph is an ear decomposition in which all ears have length in A. Similarly, an A-handle-decomposition of a digraph is a handle decomposition in which all handles have length in A. Note that an A-ear-decomposition (resp. A-handle-decomposition) of a graph (resp. digraph) can be seen as an ear decomposition (resp. handle decomposition) with no ear (resp. handle) with length in A. In view of all our results, Let A be a set of positive integers

A. Input, Question: Does G admit an A-ear-decomposition ?, A graph G

A. Input, Question: Does D admit an A-handle-decomposition ? It would be nice to characterize the graphs (resp. digraphs) for which A-EAR-DECOMPOSITION (resp. A-HANDLE-DECOMPOSITION) is polynomial-time solvable. Below is an easy lemma